Problem: Complete the equation of the line through $(-6,5)$ and $(-3,-3)$. Use exact numbers. $y=$
Explanation: Let's find the slope: $\begin{aligned} \text{Slope}&=\dfrac{-3-5}{-3-(-6)} \\\\ &=\dfrac{-8}{3} \\\\ &=-\dfrac{8}{3} \end{aligned}$ The equation is $y=-\dfrac{8}{3}x+b$ for some $b$. Let's plug the point $({-3},{-3})$ to find $b$ : $\begin{aligned} y&=-\dfrac{8}{3} x+b \\\\ {-3}&=-\dfrac{8}{3}({-3})+b \\\\ -3&=8+b \\\\ -11&=b \end{aligned}$ The equation is $y=-\dfrac{8}{3}x -11$.